If x and y are integers and √x−√y equals an odd integer, which of the

Question

If x and y are integers and √x−√y equals an odd integer, which of the following must be an even integer?

I. xy
II. x^2 + y^2
III. x/y
 
A. I only 
B. I and II 
C. II​ only 
D. I, II, and III 
E. None of these

Kurtosis · Answer

sqrt(x) - sqrt(y) = odd
sqrt(x) + sqrt(y) must also be = odd

(sqrt(x) - sqrt(y))*(sqrt(x) + sqrt(y)) = odd * odd
x - y = odd
even - odd = odd
odd - even = odd

I) xy = even? Yes. Since one term is even

II) x^2 + y^2 = even? 
x^2 + y^2 - 2xy = odd
x^2 + y^2 = odd + even = odd
So x^2 + y^2 is not even

III) x/y = even?
If x = 6 and y = 3 then yes
If x = 3 and y = 2 then no
So x/y is not always even.

Answer: A

CV7585 · Answer

If x and y are integers and √x−√y equals an odd integer, which of the following must be an even integer?

I. xy
II. x^2 + y^2
III. x/y
 
A. I only 
B. I and II 
C. II​ only 
D. I, II, and III 
E. None of these

Given that √x−√y = odd Int.

This means that one of the 2 should be odd and the other even. (Even/odd - Odd/Even = Odd). Implies x or y is even and the other is odd.

With this in mind:

I must be true - odd x even always even. (eliminate C and E).

II Not true. E + O is always odd. (Eliminate D and B).

Need not test the III.

Answer A.

Abhishek009 · Answer

\sqrt{x} - \sqrt{y} = Odd number So, X or Y can be Even / Odd; however both can not be even. Check using properties of Number system I. xy Product of an Odd and Even Number must always be Even Number II. x^2 + y^2 Square of an Odd number is Odd Number and Square of an even number is even Number Further Odd + Even Number = Odd Number III. \frac{x}{y} Now, x / y can be even / odd If x is even and y odd then \frac{x}{y} is even However if x is odd and y even then \frac{x}{y} is odd Thus using property of Number system we can find that option (A) is correct !! :-D

stonecold · Answer

Exponent does not affect the even/odd nature of x,y

Hence x-y=odd
so xy is even
x^2+y^2 is odd
 And x/y may or may not be an integer

So A

RR88 · Answer

Option A

x & y are integers such that  \sqrt{x} - \sqrt{y}  = Odd Integer
Hence, x & y must perfect squares AND  \sqrt{x}  &  \sqrt{y}  must be either Odd & Even or Even & Odd.

I. xy = E
II. x^2 + y^2 = E^2 + O^2 or O^2 + E^2 = E + O or O + E = O
III. x/y = E/O or O/E = E or O or F

bumpbot · Answer

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If x and y are integers and √x−√y equals an odd integer, which of the

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GMAT Problem Solving (PS) Questions

If x and y are integers and √x−√y equals an odd integer, which of the

Prep Toolkit

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